We used structural magnetic resonance imaging (MRI) and voxel based morphometry (VBM) to investigate whether the efficiency of word processing in the non-native language (lexical efficiency) and the number of non-native languages spoken (2+ versus 1) were related to local differences in the brain structure of bilingual and multilingual speakers. We dissociate two different correlates for non-native language processing. Firstly, multilinguals who spoke 2 or more non-native languages had higher grey matter density in the right posterior supramarginal gyrus compared to bilinguals who only spoke one non-native language. This is interpreted in relation to previous studies that have shown that grey matter density in this region is related to the number of words learnt in bilinguals relative to monolinguals and in monolingual adolescents with high versus low vocabulary. Our second result was that, in bilinguals, grey matter density in the left pars opercularis was positively related to lexical efficiency in second language use, as measured by the speed and accuracy of lexical decisions and the number of words produced in a timed verbal fluency task. Grey matter in the same region was also negatively related to the age at which the second language was acquired. This is interpreted in terms of previous findings that associated the left pars opercularis with phonetic expertise in the native language. (Contains 1 figure and 1 table.)